Start a book club for female grad students. Could attract women from other disciplines as well as other fields with few women. I suggest putting an ad up in the University Classifieds. The part time job is a good idea: if she’s willing to tutor, perhaps there’s a group of grad students who do this.
As someone who married a fellow grad student from the same department many years ago, I find the rule against intra-department dating a bit too limiting 
I do think ■■■■■■■■■■ was designed (and is marketed) specifically to address this need. I have no idea how well it works. People I know use the dating apps, but I’ve never heard anyone talk about Meetup.
All my friends in (Electrical Engineering) grad school were in my department (but it was a big department, so most were in other groups). We all met at the equivalent of orientation (again huge department – 1000 grad students at Stanford in EE). My husband came from that department also! Though we met through mutual friends. I know my husband had friends through a folk dancing group; I tried some courses at the community college later in my time there when I was “looking for love” but that was not successful! It can be tough.
A possibility that might be helpful: You could suggest that your daughter go to research seminars of interest to her in other departments than her own. For example, a physics grad student might go to math, neuroscience, and genetics seminars. Or math, electrical engineering, and (for that matter) English. Or a foreign language. Then she could strike up a conversation with another student at the seminar. Often the departments will have coffee and maybe refreshments of some type ahead of the seminars. There are sometimes foreign language clubs that show films or have events, or foreign language tables where only the foreign language is spoken at lunch. If she is not ready for those, there may be evening language classes on or off campus. Picking up an additional language is always useful, and she might meet new people. Grad organization ski trips? Trips to a nearby city for an event?
@yucca10 so far she has found relationships to be a lot of work and drama-causing. The last thing she wants is to cause department drama.
I will bring up chorus to her, it is a possibility.
I wonder about this too. My S is in a doctoral program and he says all he does is go to class, go to the gym and work/grade papers. He is in a grad student apartment but I think his neighbors are all busy (many of them med students) too.
I don’t even ask about dating. He says any activity he goes to is mostly all UG students.
Does her campus have schools like a business school or law school? Those people are probably her age and there may be events or activities she could attend to meet people. Using one of their libraries or coffeshops could work. Many of them are just as eager to have friends outside their programs as she is.
As a grad student, I was also in a male-dominated field, but bonded with and became good friends with one of the other three women in my program. We did lots of things together, and because she was more social than I was, I met a lot of other people through her. Both she and I ended up dating (and eventually marrying) fellow male grad students in our department. I was also fortunate that there were other more social groups of students in another part of the same department that often hosted potluck dinners and other activities.
One activity that I did without my friend was singing in a large University chorus that was open to both students and alumni. I met a wide range of people of all ages that way and singing was a great stress release for me. My now-husband’s favorite activity in grad school was becoming involved in an on-campus Aikido club. My son also did martial arts on campus when he was a graduate student.
I think those are great ideas, gardenstategal! And I think you are right that many grad students would like to have friends outside of their own programs.
@gardenstategal There is a business school, but no law school.
Does she like board games? Maybe she could invite several other grad students from her dept over to play some board games. That would not suggest intimate relationship and can be a low key way to get to know people. (My kids are very into board games and it is one way they have all reached out to others to start hanging out together.)
Thinking about it, I realize that a big chunk of my son’s friendship circle – which he picked up as a graduate student and as a young employee of a highly academic organization located on the campus of the university where he was a graduate student, so pretty much the same thing – comes from (a) people he met playing Netrunner (at stores, bars, tournaments), and (b) people he met at a regular Quizzo night at a local bar. Of course, these would only work if you liked Netrunner (or some other, similar game) and/or Quizzo. And the Netrunner option might not be the best way for a woman to avoid unwanted attention from immature men. But I can attest that in his mid-20s my son picked up actual, new bona fide friends that way.
She does go to bar trivia a lot, but it is with her cohort. I can attest to making friends that way – I did it this week! Went by myself to a restaurant for dinner that happened to be having trivia night. Asked a couple of I could join them for it. We had an enjoyable dinner and even won a round. 
Then I ran into them the next day on the ski trail, we chatted some more, and they invited me back to their condo for tea after skiing. They stay in this area for months each winter, and encouraged me to call next time I’m in town. I’ll certainly suggest it to her, too.
I had never heard anyone talk about Meet-Up either. I think someone on CC recommended it and I took a look at the Meet-Up web site.
In a big urban area, you’re going to find a LOT of Meet-Up groups. Well-worth a peek. It’s how I got connected to groups in my area that like to hike.
I see a lot of groups targeting young people in their 20s and 30s. Going to the first few Meet-Ups can feel awkward. But really, I’ve found, at least for my age group (mid-50s), nice people who are looking for other nice people to do things with. It doesn’t have to be your next BFF.
Didn’t read the entire thread but the Meet-Up/Sports league thing might be possible in a larger urban area. I play volleyball in a Sport and Social league in my city and I meet new 20-somethings all the time. I know you said she’s not into sports but the league has cornhole, skeeball, kickball, dodgeball and maybe more which are games and not sports. They have Free Agent teams every season for new people to sign up and meet people.
She isn’t really into sports. I’m not sure if she’ll put herself out there for a Meetup or not (and I suspect the number is smaller in her area than a lot of larger cities). But I’ll bring it up.
I’ve met a lot of interesting people on meetups. It’s really not a big deal to try a few.
Pick-up line at one of those lectures. (Surely there are better lines. But you have to start somehow.) 1. “Every time I see a Cauchy sequence, I want to get a little closer to somebody.” 2. “I try to use chemistry in my cooking, but I need someone to be my taster.” 3. “I still don’t understand how the U.S. got drawn into the Vietnam War. Can someone explain it to me? I’ll buy the coffee.”
Based on the OP’s description, his daughter isn’t looking for romance, and knows pretty well how to find it when she wants to. Even if she didn’t know, there are entire industries that exist to facilitate coupling. Finding new friends is a good deal trickier than finding new boyfriends.